Multiplicity and concentration of solutions for elliptic systems with vanishing potentials

In this article we use variational methods to study a strongly coupled elliptic system depending on a positive parameter λ. We suppose that the potentials are nonnegative and the intersection of the sets where they vanish has positive measure. A technical condition, imposed on the product of the potentials, allows us to consider a setting where we do not assume any positive lower bound for the potentials. Considering the associated functional, defined on an appropriated subspace of D1,2(RN)×D1,2(RN), we are able to establish results on the existence and multiplicity of solutions for the system when the parameter λ is sufficiently large. We also study the asymptotic behavior of these solutions when λ→∞.